Symmetry is something that most of us understand. After all, symmetrical objects are naturally pleasing to the human eye, whereas asymmetrical objects seem lightly unsatisfying for some reason. But do you know the mathematical definition of symmetry? What are the different types of symmetry? And what does symmetry teach us about math? Let's find out:
Before we get into the different types of symmetry -- including line symmetry -- let's define what this word actually means.
What is symmetry?
Symmetry stems from the ancient Greek term "symmetria," which translates roughly to "agreement in dimensions."
Symmetry essentially has two different definitions: On one hand, it may be used in a very casual manner to refer to beauty, proportionality, and harmony. On the other hand, the mathematical definition of symmetry is much more precise -- and there are specific rules regarding symmetry in geometry.
When mathematicians say that something is symmetrical, they mean that the object is "invariant." This means that it remains even if we transform it in various ways. For example, we might flip an object upside down, reverse it, or rotate it. A truly symmetrical object would remain the same no matter what we do to it.
For example, a perfect circle looks the same whether we rotate it, reverse it, or turn it upside down.
Line symmetry is the simplest form of symmetry, and it's easy to see whether objects have line symmetry.
First, divide an object into two congruent (equal) parts. Do these two equal parts look the same? Are they reflections of each other? Note that we can make our lines in any direction (horizontal, vertical, or diagonal) -- as long as the two parts are equal.
Here are a few examples of line symmetry:
Let's look at the square first. This object has a whopping four different lines of symmetry. We can divide it horizontally, vertically, and with two additional diagonal lines. All of these lines create two congruent parts.
Next, let's look at the parallelogram. This object has zero lines of symmetry. No matter how we slice it, we can't create two congruent parts that are perfect reflections of each other.
Finally, let's take a look at the rectangle. This object is clearly symmetrical -- although not quite as symmetrical as the square. As you can see, it can be divided both horizontally and vertically, giving it two different lines of symmetry. It cannot be divided horizontally to create two different congruent parts.
But what about real-world examples of line symmetry?
One obvious example is a human face -- although this isn't really true because everyone's faces are slightly asymmetrical. In fact, perfectly symmetrical faces look somewhat strange. Another obvious example is the reflection of a tree on a lake. On the other hand, this example is also slightly asymmetrical because of the ripples in the water.
Aside from line symmetry, there are a few other types of symmetry we should cover:
Here are some fun facts about symmetry:
Graphing Quadratic Equations Using the Axis of Symmetry
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